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Lubineau G.,CNRS Cachan Laboratory of mechanics and technology
International Journal of Damage Mechanics | Year: 2010

Modern approaches to the modeling of composites are no longer limited to the use of a single approach for the whole structure or for all the degradation mechanisms. On the contrary, modern advances enable the definition of truly multiscale models in order to describe the degradation. Thus, homogenized models can be rigorously deduced from the underlying micromechanics. In the past few years, LMT-Cachan has made a number of contributions to the three key points of these multiscale approaches: (1) the improvement of the reference model on the fine scale, (2) the definition of a controlled correspondence between the scales, and (3) the definition of the associated homogenized model. Here, the complete approach is formalized as a modeling pyramid. Each mechanism of degradation is described on the more relevant scale within an "hybrid micromechanical model". Based on the reference modeling, constitutive laws can be transfered within the unique framework of damage mechanics for being applied within commercial softwares. As an illustration, we focus more specifically on the homogenized law obtained for transverse cracking. The constitutive law and the material parameters issued from the homogenization, which define the model on the higher scale, are reviewed. Their identification is studied in detail. An important key point of the pyramidal approach appears here. Since it allows the interpretation of every quantity on different scales (both at the micromechanical and at the mesomechanical scales), the most relevant scale can be used for the identification of a chosen property. We limit ourselves to a "classical" identification. We mean by classical identification a procedure based on straight specimens. This process, to a certain extent, uses a parametric simulation of the nonlinear model based on a finite element representation of the test samples. The complete model is then used for the simulation of an industrial sample with hole. That example emphasizes the interest of underlying micromechanial variables for experimental validation. © The Author(s), 2010. Source

Choukairy K.,University Hassan 1 | Bennacer R.,CNRS Cachan Laboratory of mechanics and technology
Fluid Dynamics and Materials Processing | Year: 2012

This study carries the natural thermosolutal convection induced in heterogeneous porous media. The configuration considered is cartesian. The horizontal and vertical walls are submitted to different mass and heat transfer. The equations which govern this type of flow are solved numerically by using the finite volume method. The flow is considered two-dimensional and laminar. The model of Darcy and the approximation of the Boussinesq are taken into account. The parametr which control the problem are the thermal Darcy-Rayleigh number, Rt, the buoyancy ratio, N, the Lewis number, Le, the aspect ratio of the enclosure, A and the local permeability ratio, K r The flow fields, temperature and concentration are given for various values of the local permeability. The effects of increasing the local permeability, the thermal Darcy-Rayleigh number Rt and buoyancy ratio, N on the heat and mass transfer are discussed. These numerical results were confirmed analytically by using the parallel flow approximation. A good agreement was found between the two analytical and numerical approaches, which confirm the validity of the analytical approach in such heterogeneous domain. The flow intensity and transfer increase with the increase of the permeable heterogeneity of the domain. © 2012 Tech Science Press. Source

Bohinc U.,Slovenian National Building And Civil Engineering Institute | Brank B.,University of Ljubljana | Ibrahimbegovics A.,CNRS Cachan Laboratory of mechanics and technology
Computer Methods in Applied Mechanics and Engineering | Year: 2014

We provide in this work the discretization error estimates that can guide an adaptive mesh refinement for the Discrete Kirchhoff plate finite elements. The proposed developments are built upon the concept of error estimates for classical elasticity and adapted to suit the Kirchhoff plate finite elements. We give a detailed illustration of the proposed procedures for the Discrete Kirchhoff triangular plate element, along with several different possibilities for constructing the enhancement of test space needed for error estimates. The first novelty concerns the consistent displacement field in terms of the third order polynomial for the Discrete Kirchhoff triangle, whereas the second novelty is the use of the Argyris triangle with fifth order polynomials for constructing the enhanced test for error estimates. We compare the latter against several alternatives that can be used for Kirchhoff plates. The results of numerical examples are given to illustrate the effectiveness of proposed discretization error estimates. © 2013 Elsevier B.V. Source

Gant F.,CNRS Cachan Laboratory of mechanics and technology | Rouch Ph.,Laboratoire Of Biomecanique | Champaney L.,Arts et Metiers ParisTech
Computers and Structures | Year: 2013

The objective of this work is to develop a modeling strategy for assemblies involving multiple joints in an aeronautical predesign context. In the process of designing large structures, industrial engineers usually get around computational limitations by using submodeling techniques. When dealing with uncertain parameters, additional numerical difficulties appear due to the increase in the problem's size. In order to consider phenomena which vary during the global representation of the submodeling process, we propose a modeling approach for the scattering of these phenomena based on the Lack-Of-Knowledge theory. The proposed strategy is illustrated by the case of a multiple-joint assembly. © 2013 Elsevier Ltd. All rights reserved. Source

Gant F.,CNRS Cachan Laboratory of mechanics and technology | Rouch Ph.,Laboratoire Of Biomecanique | Louf F.,CNRS Cachan Laboratory of mechanics and technology | Champaney L.,CNRS Cachan Laboratory of mechanics and technology
International Journal of Solids and Structures | Year: 2011

The objective of this work is to define a simple linear model of joints used in aeronautics and to update this model efficiently. Industrial designers usually resort to semi-empirical linear joint models to represent the behavior of the joints of a large aeronautical structure. Here, we propose to develop a one-dimensional linear joint model which is capable of representing the behavior of every joint of a large structure globally while enabling local nonlinear reanalysis of the most highly loaded joints. Work on nonlinear reanalysis is not considered in this paper. In order to solve the numerical difficulties encountered in some of modeling situations, an updating strategy based on the constitutive relation error is proposed. Since the updating efficiency is significantly affected by the ratios of the stiffnesses of the different parts of the model, the strategy consists in rigidifying some parts of the model in order to control the updating accuracy and the rate of convergence. The numerical results of a standard model and a rigidified model illustrate the updating improvements allowed by the strategy. © 2010 Elsevier Ltd. All rights reserved. Source

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